Aliquot sum

In number theory, the aliquot sums(n) of a positive integern is the sum of all proper divisors of n, that is, all divisors of n other than n itself. That is, $${\displaystyle s(n)=\sum _{{d|n,} \atop {d eq n}}d\,.}$$

It can be used to characterize the prime numbers, perfect numbers, sociable numbers, deficient numbers, abundant numbers, and untouchable numbers, and to define the aliquot sequence of a number.